I will merely point out that this quote from Freedman (which I take as representative of your views)
Blockquote
For thirty years, I have found Bayesian statistics to be a rich source of mathematical questions. However, I no longer see it as the preferred way to do applied statistics, because I find that uncertainty can rarely be quantified as probability.
is different from this:
Blockquote
The successful users of probability models should consider them simply as fallible tools to help them think of more questions and provide directions for seeking more information and data, not turn-the-crank machines that provide risk management recipes free of shoe leather and critical thinking.
No one (especially not me) argued for the latter. To do so would be engaging in the practice of
“persuasion and intimidation” that Stark properly condemns. Unfortunately, I find much of “evidence based” rhetoric accurately described by his language.
I believe I’ve shown via the example of extracting the implied probabilities from options prices, that even decision makers at the highest levels, in a regime of incomplete markets, find valuable information contained in a subjective, betting odds interpretation of probability that has no physical meaning.
Indeed, I consider precise probability models merely as a point of reference to compute the width of the range of interval probabilities (aka covering priors) worth considering.
Related Thread